If you want the tattoo to be large and extravagant, then your back is the ideal place, since it is the largest and relatively flattest portion of your body and can be easily covered by clothing for professional or other purposes. The script can either span your upper back, laying between your shoulder blades, or go straight down your spine, symbolizing an ancestral backbone. Connecting fonts are harder to accomplish with vertical script, so each letter in a spine tattoo may need to be independent.
The outer forearm of either arm, from the elbow to the pinky side of your wrist, can also be an ideal spot for a last name tattoo. The area is relatively flat and straight, but also large enough to fit a decoratively intermediate font. You can have the letters laid horizontally or vertically, depending on your preference, and either spanning completely from elbow to wrist or in any portion in between. Also, if necessary, a long-sleeve shirt can easily cover this tattoo.
Most respectable tattoo artists will not tattoo something that should be, but cannot be viewed in its entirety, such as a last name wrapping completely around your thigh or ankle. However, if that is a style you desire, you can have the tattoo span only a quarter length around your thigh or calf, so it can be seen in its entirety but still curve around your leg. Others can simply use the vertical-style tattoo running down any portion of your leg. For professional and other purposes, leg tattoos can also be easily covered.
Any neck tattoo carries certain difficulties in functionality, as it can almost never be covered completely by clothing. But if you are willing to take on the commitment of having an always-visible tattoo, consider a beautiful, non-threatening script of your last name on either the right or left side, depending on your dominant hand. The word should be at an angle that matches your jaw line. Although traditional script tattoos are done in black and gray, you may wish to use color for a neck tattoo to make it less threatening.